ac fuse blows

The most likely cause for the a/c fuse blowing in your 2006 Chevrolet Monte Carlo would be an intermittent fault with the compressor clutch coil on your a/c compressor. Either a damaged wire is shorting to ground or the a/c clutch coil is drawing to much current and blowing the fuse. In most cases the clutch coil comes with a new compressor. If a visual inspection of the wiring from the a/c relay to the a/c compressor shows no damaged wires then replacing the compressor as a "best guess" may be the next step in "diagnosing" this problem.